It is believed that hitherto, the obvious, realistically useful way to lay out a three-dimensional display comprising light emitting diodes has been to utilize identical layers (e.g., a two-dimensional OLED display) that repeat directly upwardly in the z axis, one atop the next. This has been done at least since U.S. Pat. No. 5,929,572 to Whitesell and GB Patent Application 2376555 to Eickhoff, through U.S. Patent Application Publication No. 2004/0145538 to Uchida et al., U.S. Pat. No. 6,720,961 to Tracy, U.S. Patent Application Publication No. 2009/0002266 (now issued as U.S. Pat. No. 8,525,954) to Li et al., and U.S. Pat. No. 7,587,120 to Koo et al.
Work in the LED television and monitor field, though extensive, is ‘pixel-centric’ (and likely moreso with OLED's rise), and conventional two-dimensional pixels arrays are not prone to being stacked to create a three-dimensional volumetric display in any arrangement other than identical, direct stacks. Further, it is believed that where those in the field have deliberately controlled the relative distancing of layers from one another in stacked volumetric displays (e.g., DE 102008007287), it has been for purposes other than (and not consistent with) establishing a three-dimensionally regular voxel or a three-dimensionally even element spacing.
Even if one in the field had contemplated trying to depart from the existing model, and if they happened to consider the notion of space-filling in the process, the possibility of employing an arrangement of elements that is derived from the geometry of the close-packing of spheres would not have appeared to be a good candidate. For one thing, a spherical voxel would be impractical to construct. (A voxel might be formed of a spherical-shaped diffusing material, but the opacity of the resulting extent of diffusing material is not desirable for a volumetric three-dimensional display, if not untenable depending on the density and depth of elements). In any case, when densely-packed, equal spheres leave numerous gaps of two different shapes and only fill about 74% of space; similarly with the regular tetrahedrons that are formed by connecting the centerpoints of close-packed equal spheres. Further, the standard group of emitters used to generate full color (e.g., 256+ colors) LED displays comprises three emitters (red, green, and blue, or RGB), with other groups that consist of more or less than three emitters now receiving comparatively little (and often diminishing) attention; if a space-filling approach would have been entertained hitherto, the approach would also have been repelled by the lack of advantage to laying out R, G, and B emitters in a three-dimensional pattern.